Mathematical Modeling of the Colorectal Myoelectrical Activity in Humans

Measurement of the colorectal myoelectrical activity in humans has revealed three basic patterns of behavior, comprising a lower frequency oscillation of about 0.05 Hz, a higher frequency of about 0.12 Hz and periods of zero activity. To simulate these myoelectrical patterns, the concept of linked relaxation oscillators is extended in this paper using three different mathematical model structures. In the three models two of the activity patterns are obtained as two stable limit cycle solutions produced by symmetrically coupling together two relaxation oscillators. The first model comprises a ring of interconnected oscillators which produces a third stable solution representing the higher frequency of oscillation. Summation of adjacent oscillator outputs reproduces the zero activity when the oscillators are in antiphase. By addition of an extra coefficient into the basic relaxation oscillator equation for the second model, the zero state becomes a stable condition and the three patterns are obtained without the necessity of a ring structure. The third model requires an in-situ change in a parameter value for the lower and higher frequencies to decay away to the zero activity condition.